Propellant is a key resource in a satellite. Once placed in orbit, a satellite typically cannot be refueled. Therefore, the functional life of a satellite is directly dependent on the amount of propellant remaining in the satellite. Most satellites remain useful, and accordingly are not replaced by new satellites, until their propellant runs out. The enormous expense to build, launch and operate a satellite in orbit means that accurate estimation of remaining propellant, also referred to as fuel, is critically important, both from a cost standpoint and an operational standpoint. A satellite is typically designed to carry enough propellant to last through its design life plus enough additional propellant to move it out of its service orbit. For a satellite in a geosynchronous service orbit, the typical approach to moving the satellite out of its service orbit is to fire its thrusters to cause it to slow and thereby move to a higher orbit, for example a super-synchronous orbit that is typically a few hundred kilometers above the geosynchronous orbit altitude.
Long term monitoring of propellant levels can be important in facilitating an accurate prediction of when just enough propellant remains to perform final maneuvering operations to move the satellite out of its service orbit. Miscalculations of the remaining propellant in either direction can be quite undesirable. Over-estimation of the remaining propellant can lead to the highly undesirable outcome of not being able to maneuver the satellite out of its service orbit and lacking any further energy source for controlling the satellite. Conversely, under-estimation of the remaining propellant can lead to prematurely removing the satellite from its service orbit despite adequate propellant remaining for continued operation. In light of the current inaccuracies in measurement of remaining propellant, a margin of error or safety factor is usually taken into account to ensure that an over-estimation of remaining propellant can be avoided. Improved accuracy and precision of remaining propellant measurement techniques could lead to substantial savings by reducing the safety factor that is required to avoid a satellite lacking sufficient propellant at the end of its useful life to be capable of being removed from its service orbit.
The propellant of a satellite is typically a liquid, such as for example liquid hydrazine (N2H4), which is pressurized in one or more propellant tanks by a non-reactive pressurant, such as for example nitrogen gas (N2). The propellant tanks are usually connected to each other and to the propulsion thrusters by a number of valves, which can be operated to direct propellant from any of the one or more propellant tanks to any of the propulsion thrusters, or selectively isolate one or more of the propellant tanks from all thrusters and from the remaining propellant tanks. Various techniques have been used for estimating the amount of propellant remaining in a satellite. One such technique, traditionally known as the PVT method, employs the ideal gas law. As illustrated with reference to the system 100 shown in FIG. 1, the pressure (P) and temperature (T) of a pressurant 102 within a propellant tank 104 are used to infer the ullage volume (V) within the propellant tank 104. From the inferred ullage volume and the known physical volume of the propellant tank 104, the remaining volume of propellant 106 can be calculated. For clarity, the term “ullage volume” refers to the physical volume of a loaded tank 104 of liquid propellant in excess of the volume of the propellant 106 remaining in the tank 104. As liquid propellant 106 is drawn from the propellant tank 104, the ullage volume increases. One or more pressure transducers and one or more temperature sensors in the propellant tank 104 measure, respectively, the pressurant pressures and temperatures within the propellant tank, which can be used to estimate the ullage volume using the ideal gas law assuming a constant amount of pressurant gas. The ullage volume can be used to determine the amount of propellant remaining in each propellant tank by difference with the tank's physical volume as illustrated by the relationship 110 shown in FIG. 1.
The accuracy with which the amount of propellant remaining in a satellite can be estimated using the PVT method depends, in great part, on the accuracy of pressurant pressure and temperature measurements. Most pressure transducers experience a phenomenon of physical degradation known as “drift” that causes the accuracy of their measurements to vary as a function of time. Unaccounted for, pressure transducer drift may result in propellant estimation accuracy degradation, which worsens over time. Further, to conserve weight, power consumption, and communication bandwidth required by telemetry data, most conventional pressure transducers used on satellites have a large quantization step size, which can further erode pressure measurement accuracy and, as a result, propellant estimation accuracy. A drift in the reading of such a pressure transducer over time can be difficult to quantify with large quantization step sizes, because changes on a scale smaller than the quantization step are generally unresolvable.
Improvements in propellant estimation accuracy can be achieved if the effects of large pressure transducer quantization step size can be mitigated and the pressure transducer drift can be estimated, or at least bounded, by some means. In most PVT implementations, pressure transducer drift is usually inferred from statistical analysis of factory measurement data, which can be unreliable. Another problem with factory drift characterization is that it is derived from past measurements on the ground, which may not be reflective of how a specific pressure transducer actually behaves on a satellite in orbit.
An improved conventional approach to characterizing pressure transducer drift involves measuring it as part of satellite orbital operations. This method of drift estimation requires that the tank in which the pressure transducer to be characterized resides be isolated to produce an isochoric, or constant-volume, thermodynamic process. The drift statistics can then be inferred from isochoric pressure telemetry. If the drift rate is small relative to the pressure transducer quantization step size, however, very long observation periods (possibly many years) may be required for the drift to manifest into observable changes in pressure telemetry. For instance, a transducer with a 2.0 psi step size, which drifts at an average rate of 0.2 psi/year, may require up to 10 years to register a change in its reading of a constant pressure. For many satellites, such long periods of tank isolation are impractical.
Another propellant estimation technique is known as the thermal capacitance method (TCM). Most TCM implementations rely on heaters, which add to the satellite weight, cost and power consumption, to deliver an amount of heat to the propellant tank to cause a measurable change in temperature. The TCM technique measures the heat capacity ΔQ/ΔT of the propellant remaining in a propellant tank (in other words, the amount of heat ΔQ required to change the propellant temperature by ΔT). Because the specific heat (i.e. the heat capacity per unit mass) of the propellant is well known, the propellant mass can be inferred based on a measured change in temperature (e.g. in ° C.) for a given transfer of heat (e.g. in Joules, Kilojoules, etc.) to the propellant. There are other variations of this method, which may or may not involve propellant tank heaters. However all rely on essentially the same principle. Accurate propellant estimation using TCM usually requires very accurate satellite thermal models, which may not always be practical.